A formula was derived for the prediction of the response to recurrent selection when the effective population size (Ne) is small. Usually, responses to selection have been estimated by Rs = icsigma²A/sigmaPh, where i, c, sigma²A, and sigmaPh stand for standardized selection differential, parental control, additive variance, and phenotypic standard deviation, respectively. This expression, however, was derived under the assumption of infinite population size. By introducing the effects of finite population size, the expression derived was Rs = [ic(sigma²A + deltaFD1)/sigmaPh] - DFID, where deltaF, ID and D1 are the changes in the inbreeding coefficient, the inbreeding depression, and the covariance of additive and homozygous dominance effects, respectively. Thus, the predicted responses to selection based on these expressions will be smaller than those based on the standard procedures for traits with a high level of dominance such as yield. Responses to five cycles of half-sib selection were predicted for maize by both expressions, considering that 100 progenies were evaluated and 10 S1 progenies were recombined, which corresponds to Ne = 10 for each cycle. The accumulated response to selection estimated with the new expression was about 47 and 28% smaller than that based on the standard expression for yield and plant height, respectively. Thus, the expression usually used overestimates the responses to selection, which is in agreement with reported results, because it does not take into account the effective population size that is generally small in recurrent selection programs
